Reflected Brownian Motions in the KPZ Universality Class
This book presents a detailed study of a system of interacting Brownian motions in one dimension. The interaction is point-like such that the n-th Brownian motion is reflected from the Brownian motion with label n-1. This model belongs to the Kardar-Parisi-Zhang (KPZ) universality class. In fact, be...
Κύριοι συγγραφείς: | , , |
---|---|
Συγγραφή απο Οργανισμό/Αρχή: | |
Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
Γλώσσα: | English |
Έκδοση: |
Cham :
Springer International Publishing : Imprint: Springer,
2017.
|
Σειρά: | SpringerBriefs in Mathematical Physics,
18 |
Θέματα: | |
Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- Introduction
- One-sided reflected Brownian motions and related models
- Skorokhod construction
- Packed initial conditions
- Infinite particle systems
- Determinantal point processes
- Definition
- Fredholm determinants
- Correlation kernel
- Strategy for future proofs.-Airy processes.-Elementary Airy processes
- Crossover Processes
- Variational identities
- Gaussian fluctuations of the Airy_stat process
- Packed and Periodic initial conditions
- Packed initial conditions
- Periodic initial conditions
- Stationary initial conditions
- Poisson initial conditions
- Determinantal structure
- Asymptotic analysis
- Path-integral style formula
- Analytic continuation
- More general initial conditions and their asymptotics
- Half-Periodic initial conditions
- Half-Poisson initial conditions
- Poisson-Periodic initial conditions
- Attractiveness and a more general class of initial data
- Asymptotics along space-like paths and slow decorrelations
- References.